Many recent ILP systems are meta-level systems [1]}.
These approaches encode the ILP problem as a meta-level logic program, i.e. a program that reasons about programs.
Meta-level approaches often delegate the search for a solution to an off-the-shelf solver [2]}, [3]}, [4]}, [5]}, [6]}, [7]} after which the meta-level solution is translated back to a standard solution for the ILP task.
For instance, ASPAL translates an ILP task into a meta-level ASP program that describes every example and every possible rule in the hypothesis space.
ASPAL then delegates the search to an ASP system to find a subset of the rules that covers all the positive but none of the negative examples.
Meta-level approaches can more easily learn recursive programs and optimal programs.
